Robustifying Conditional Portfolio Decisions via Optimal Transport

We propose a data-driven portfolio selection model that integrates side informa-tion, conditional estimation, and robustness using the framework of distributionally robust optimization. Conditioning on the observed side information, the portfolio manager solves an allocation problem that minimizes the worst-case conditional risk-return tradeoff, subject to all possible perturbations of the covariate-return probability distribution in an optimal transport ambiguity set. Despite the nonlinearity of the objective function in the probability measure, we show that the distributionally robust portfolio allocation with a side information problem can be reformulated as a finite-dimensional optimization problem. If portfolio decisions are made based on either the mean-variance or the mean-conditional value-at-risk criterion, the reformulation can be further simplified to second-order or semidefinite cone programs. Empirical studies in the U.S. equity market demonstrate the advantage of our integrative framework against other benchmarks.